Torsion members - The Behaviour and Design of Steel Structures to EC3 - page 458

Twist rotation and
warping prevented
0 = 0 = 0

(+)

T

Free to warp
L = 0

(b) Torque T x

T

T

T L
GI t

1- e -2 L/a

a
L

x

1-

(+)

1+ e -2 L/a

L

(a) Cantilever

(c) Twist rotation

Figure 10.28 Non-uniform torsion of a cantilever.

angleoftwistrotationobtainedbysolvingequation10.48.Valuesof φ tm and φ wm
can be obtained from Figures 10.20 and 10.21 for a number of different torsion
members.
Thisapproximatemethodtendstooverestimatethetruemaximumangleoftwist
rotation,partlybecausethemaximumvalues φ tm and φ wm oftenoccuratdifferent
locations along the member. In the case of the cantilever of Figure 10.28, the
approximate solution

TL / GI t
1 + 3 EI w / GI t L 2

φ m = (10.57)

obtainedusingFigures10.15cand10.25cinequation10.56hasamaximumerror
of about 12% [17].

10.3.3 Plastic collapse analysis

10.3.3.1 Fully plastic bimoment

The warping normal stresses σ w developed in elastic warping torsion are usually
muchlargerthanthewarpingshearstresses τ w .Thusthelimitofelasticbehaviour
is often reached when the bimoment is close to its nominal first yield value for
which the maximum value of σ w is equal to the yield stress f y .
FortheequalflangedI-sectionshowninFigure10.24,thefirstyieldbimoment
B y corresponds to the flange moment M f reaching the yield value

M fy = f y b f t f / 6 (10.58)

so that

B y = f y d f b f t f / 6

(10.59)

in which b f is the flange width, t f is the flange thickness, and d f is the dis-
tance between flange centroids. As the bimoment increases above B y , yielding